An AR model may be used during signal processing as a representation or model of a type of random or stochastic process to describe certain time-varying processes. The AR model specifies that an output variable depends linearly on its own previous values and on a stochastic term, thus the AR model is in the form of a stochastic difference equation.
For an auto-covariance or autocorrelation function of a random process, a typical method of obtaining AR parameters is by solving a Yule-Walker (YW) equation. Using this approach, an AR model with lag p can exactly reproduce a stochastic process with identical correlations up to length p, where p is an integer. A typical AR parameter estimation method can exactly match autocorrelations up to a length p assuming that a pth order AR model is used. Therefore, to model long correlations, a large p is required, which typically indicates increased complexity and inefficiency.